一类相依双险种风险模型的罚金折现期望函数  

The Expected Discounted Penalty Function in a Kind of Department Risk Model with Double-type-insurance

作　　者：聂高琴[1] 刘次华[2] 

机构地区：[1]首都经济贸易大学统计学院,北京100070 [2]华中科技大学数学与统计学院,湖北武汉430074

出　　处：《数学的实践与认识》2010年第4期68-75,共8页Mathematics in Practice and Theory

基　　金：北京市自然科学基金(70073018);首都经济贸易大学校内项目(2009XJ014)

摘　　要：考虑索赔到达具有相依性的一类双险种风险模型,其中第一类险种的索赔计数过程为Poisson过程,第二类险种的索赔计数过程为其p-稀疏过程与广义Erlang(2)过程的和,利用更新论证得到了此风险模型的罚金折现期望函数满足的微积分方程及其Laplace变换的表达式.并就索赔额均服从指数分布的情形,给出了罚金函数及破产概率的精确表达式.We consider a risk odel involving two dependent classed of claims arrivals, where the claim number process of the first class is Poisson process, and the second is the sum of its p-thinning process and generalized Erlang （2） process. We get the integro-differential equation satisfied by the expected discounted penalty function by the renewal argument, and Laplace transform of it is derived from the equation. Explicit results of the penalty function and the ruin probability axe derived when the claims from both classes axe exponentially distributed.

关 键 词：广义Erlang(2)过程 p-稀疏过程 罚金折现期望 LAPLACE变换 破产概率 

分 类 号：F224[经济管理—国民经济] F840